In ultra-short pulsed laser systems the active laser crystals (semiconductor or dielectric) with laser-active dopants are used as the laser gain media as well as simultaneously as the nonlinear media for generation of ultrashort-pulses by various passive- and passive/active mode-locking mechanisms. Very often these crystals possess high optical nonlinearity, both second order and third order. This is, for example, the case in zinc-blende and wurtzite semiconductors and in particular, in transition-metal-doped chalcogenides, where the second order and third order nonlinearities coexist.
The generation of the second harmonic during the propagation of an ultrashort pulse inside a dispersive medium (both phase-matched and non-phase-matched) is accompanied by accumulation of a group delay between the fundamental and the second harmonic waves due to a naturally occurring group velocity mismatch between the two wavelengths.
For a non-phase-matched crystal, where the second harmonic signal for a monochromatic wave would periodically back-convert to the fundamental and return to zero at propagation distances equal to even number of coherence lengths, this group velocity mismatch would result in a constant increase of the second harmonic generation intensity, because the group delay prevents complete back-conversion of the second harmonic wave to the fundamental. In the case of typical dispersion values in dense media the group-velocity mismatch may be of the order of hundreds of femtoseconds per millimetre of propagation distance.
For an ultrashort pulse with duration of shorter than a few hundred femtoseconds, the second-harmonic signal turns to a long tail that drags behind the fundamental pulse, only partially overlapping with it in time. In case of a picosecond-scale chirped pulse, the second harmonic signal generally has better overlap with the chirped fundamental pulse, and interaction of the generated and retarded second harmonic radiation with the chirped fundamental becomes even more involved and may result in spectral and temporal modulation of the fundamental pulse.
In a typical mode-locked solid-state laser cavity, or in a regenerative or multi-pass amplifier with at least one mirror being physically separated from the crystal, both second harmonic and fundamental pulses will re-enter the crystal with an additional phase and group delay accumulated during the propagation in the free space (e.g. atmosphere), dispersion-compensating elements, and the mirror coatings. After re-entrance into the crystal, the second harmonic generation will resume, with the sign and efficiency depending upon the accumulated delays. This process thus becomes sensitive to the mirror and crystal positions, ambient temperature, insertion of the wedged elements, etc., and can result in saturable or inverse saturable absorber effect (see for example K. A. Stankov, “A mirror with an intensity-dependent reflection coefficient,” Appl. Phys. B 45, 191-195 (1988)). This may cause disruption of mode-locking, spectral and temporal modulation of the pulse, and may strongly increase the environmental sensitivity of the system.
The efficiency of fundamental to second harmonic conversion increases with peak intensity (pulse shortening and/or energy increase) and may reach a few percent already in low power Cr:ZnSe (or Cr:ZnS) modelocked oscillators with a pulse duration of the order of 100 femtoseconds (see for example, E. Sorokin, N. Tolstik and I. T. Sorokina “Femtosecond operation and self-doubling of Cr:ZnS laser” at Nonlinear Optics' 2011 conference, OSA Technical Didest, paper NTHC1; and E. Sorokin, I. T. Sorokina “Femtosecond operation and random quasi-phase-matched self-doubling of ceramic Cr:ZnSe laser”, OSA Technical Digest, paper CTUGG2 at Conference on Lasers and Electrooptics CLEO'2010). For higher energies and/or shorter pulses this conversion efficiency may become even higher, starting to compete with the mode-locking mechanism and causing pulse break-up, etc. Growth of the second harmonic conversion efficiency with peak power is equivalent to an inverse saturable absorber acting on the pulse at fundamental wavelength.
When a polycrystalline material is used, besides the main pulse at the fundamental wavelength, the laser emits radiation also at the second harmonic wavelength (see for example E. Sorokin, N. Tolstik and I. T. Sorokina “Femtosecond operation and self-doubling of Cr:ZnS laser” at Nonlinear Optics′2011 conference, OSA Technical Didest, paper NTHC1; and E. Sorokin, I. T. Sorokina “Femtosecond operation and random quasi-phase-matched self-doubling of ceramic Cr:ZnSe laser”, OSA Technical Digest, paper CTUGG2 at Conference on Lasers and Electrooptics CLEO'2010).